Witti-Buch2 2001.qxd - Austrian Ludwig Wittgenstein Society

Is Logic Syntax of Language?
Carnap's Programme, Gödel's Critique,
and Wittgenstein's Evasion
Brian David Mogck
The purpose of this paper is to show that Wittgenstein developed a theory of logical
syntax that is in several important respects identical to Carnap's. Gödel's criticism of
Carnap's project (bearing on consistency) is considered. It is then shown how
Wittgenstein's logical syntax avoids this criticism. In conclusion, it is suggested in
response to Gödel's criticism that logical syntax aims at descriptive, not semantical
completeness.
1. Logical Syntax in Carnap and Wittgenstein
It has not widely been appreciated that Wittgenstein's middle-period logical theory was
in substantial agreement with Carnap's logical syntax. 1 Wittgenstein, in a discussion with
members of the Vienna Circle circa 1930, states that "[p]hilosophy is the clarification of
the syntax of language." 2 This is four years before Carnap completed his Logical Syntax
of Language. In fact, Carnap wrote to Neurath on December 23, 1933, "My syntax
historically has two roots: the first is Wittgenstein, the second is metamathematics." 3
Four theses define the core of this syntax.
1.1 Logic is a Formal Study of Linguistic Structures
This thesis amounts to holding that logical properties and relations are properties
and relations of signs and not of their meanings. These properties and relations are
known a priori by considering the formal structure of sentences, that is, how they are
legitimately formed and transformed. For Carnap, "[i]t was Wittgenstein who first
exhibited the close connection between the logic of science (or 'philosophy, as he calls
it) and syntax. In particular he made clear the formal nature of logic and emphasized
the fact that the rules and proofs of syntax should have no reference to the meaning of
symbols." (LSL, p. 282)
A likely source for this view is TLP 3.33: "In logical syntax the meaning of a sign
should never play a rôle. It must be possible to establish logical syntax without
mentioning the meaning of a sign; only the description of expressions may be
presupposed." (Cf. 4.1213) In fact, for Wittgenstein the whole philosophy logic is
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